Due to the increasing complexity of today's circuits a high degree of automation in the design process is mandatory. The detection of faults and design errors is supported quite well using simulation or formal verification. But locating the fault site is typically a time consuming manual task. Techniques to automate debugging and diagnosis have been proposed. Approaches based on Boolean Satisfiability (SAT) have been demonstrated to be very effective. In this work debugging on the gate level is considered. Unsatisfiable cores contained in a SAT instance for debugging are used (1) to determine all suspects, and (2) to speed-up the debugging process. In comparison to standard SAT-based debugging, the experimental results show a significant speed-up for debugging multiple faults. Categories and Subject Descriptors B.6.3 [Hardware]: LOGIC DESIGN--Design Aids General Terms Design, Verification Keywords SAT-based debugging, Fault Localization, Unsatisfiable Core